C2 chapter 4 - coordinate geometry

In this chapter we learn how to find the mid-point of a line segment, the distance between two points in the plane, the equation of a circle. We will also use the properties of a circle to solve geometric problems.
Chapter overview


Three presentations to help you memorize the circle theorems

C2 section 4.1a

You need to be able to: be able to find a simple average.

We are learning to find the midpoint of a line segment.
Given points A and B with coordinates (p,q) and (r,s) respectively, the midpoint of the line segment AB is given by
$\displaystyle \left( \dfrac{p + r}{2} , \dfrac{q + s}{2} \right)$

This is frequently used in connection with circles: where AB is a diameter, its midpoint will be the centre of the circle.
Examples:

C2 Exercise 4A

• C2 Exercise 4A worked solutions:

C2 Exercise 4A (mid-point of segment).pdf

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C2 Exercise 4A (mid-point of segment).jnt

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• Questions similar to this exercise:

You need to be able to: be able to find the gradient of a perpendicular line and find the equation of a line given gradient and a point on the line. You may wish to revise C1 chapter 5.

C2 section 4.1b

We are learning to use midpoints of diameters to solve problems involving circles, chords and diameters.

C2 exercise 4B

• C2 Exercise 4A worked solutions:

• Questions similar to this exercise:

C2 section 4.2

You need to be able to: be able to find a simple average.

We are learning to find the midpoint of a line segment.

C2 exercise 4C

C2 section 4.3

C2 exercise 4D
C2 exercise 4E

C2 Exercise 4F